This study will evaluate the pharmacokinetics and tolerance of ZDV in premature infants. 35 premature infants whose gestational age is less than or equal to 34 weeks will be enrolled in the study. All subjects enrolled will initially receive ZDV for a period of 6 weeks at an initial dose of 1.5 mg/kg IV or PO every 12 hours. Real time pharmacogentetic samples will be obtained three times after initiation of study drug. ZDV dosage will be modified based upon the results to the ZDV through concentration.